answer the questions below about the quadratic function
a. does the function have a minimum or maximum value
b. what is the function's min or max value
c. where does it occur x=
Thank you for the opportunity to help you with your question!
NB I am assuming that you erroneously ignored the x in 8x.
To determine whether the function has a maximum or minimum, we differentate it twice i.e
first derivative, g'(x) = 2x+8
Second derivative, g"(x) = 2
Therefore the function has a minimum point since the second derivative is positive i.e (+2)
The function minimum point is the point where the slope/gradient of the function is equal to zero.
The slope/gradient of the function is given by the first derivative
Therefore, g'(x) = 2x+8 = 0
2x =-8 hence x=-4
Substituting the value of X into the equation gives
g(x) = (-4)^2+8(-4)+18 = 2
Therefore the functions minimum point is 2
As calculated above, the function's minimum point occurs at the point where x= -4
Let me know if my assumption of instituting x into the function was right or wrong.Regards.
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